The Houston Chronicle has published a list of "Ten things about Rick Perry that may worry some conservatives." Some items are stronger than others, but expect to hear immigration come up. Although he's called for troops on the Mexican border and cracking down on sanctuary cities, he's also been sympathetic to DREAM Act-style policies while distancing himself from Arizona's SB 1070.
From the Chronicle story: "'During his time as governor of Texas, Rick Perry consistently supported allowing illegal aliens to pay in-state tuition at Texas' state colleges and universities,' says an assessment of Perry's immigration record by NumbersUSA." The restrictionist group gives Perry a D minus on the issue.
Of course, George W. Bush and John McCain were both prominent advocates of "comprehensive immigration reform" and this rather conspicuously did not prevent them from being nominated.